= Barotropic closure of a razor-thin disk
{title2=$c_s^2=dP/d\Sigma$}
A two-dimensional disk equation with <pressure> acceleration $-\Sigma^{-1}\nabla P$ requires an equation of state for vertically integrated <pressure> $P$ in terms of <surface density of a disk> $\Sigma$. A <barotropic fluid> closure is $P=P(\Sigma)$, with linear enthalpy perturbation $h'=c_s^2\Sigma'/\Sigma_0$. Merely giving $P=P(\rho)$ for a volume density does not close the two-dimensional equations unless a vertical conversion $\rho(\Sigma)$ is specified. Positive $c_s^2$ gives ordinary <pressure> restoration of an <inertial-acoustic wave>.
Back to article page
